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3/2003 Rev 1 I.3.1-2 – slide 1 of 20 Part I Review of Fundamentals Module 3Interaction of Radiation with Matter Sessions 1-2Heavy Particles Session I.3.1-2 IAEA Post Graduate Educational Course Radiation Protection and Safety of Radiation Sources

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3/2003 Rev 1 I.3.1-2 – slide 2 of 20 Upon completion of this section, the student should have an understanding of the following interactions for heavy particles: Bragg curve Stopping power Shielding Overview

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3/2003 Rev 1 I.3.1-2 – slide 3 of 20 When a charged particle interacts with an atom, it may: traverse in close proximity to the atom (called a “hard” collision) traverse at a significant distance from the atom (called a “soft” collision) A hard collision will impart more energy to the material than a soft collision Particle Interactions

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3/2003 Rev 1 I.3.1-2 – slide 4 of 20 Bragg Curve - Alpha Alpha Particle Beta Path

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3/2003 Rev 1 I.3.1-2 – slide 5 of 20 Bragg Curve - Proton

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3/2003 Rev 1 I.3.1-2 – slide 6 of 20 Absorbed dose is energy imparted per unit mass of material: The unit of absorbed dose is the Gray (Gy) (1 Gray = 1 joule/kg) To calculate the dose from charged particles, we need to determine the amount of energy deposited per gram of material Absorbed Dose

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3/2003 Rev 1 I.3.1-2 – slide 7 of 20 The amount of energy deposited will be the sum of energy deposited from hard and soft collisions The “stopping power,” S, is the sum of energy deposited for soft and hard collisions Most of the energy deposited will be from soft collisions since it is less likely that a particle will interact with the nucleus Stopping Power

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3/2003 Rev 1 I.3.1-2 – slide 8 of 20 The stopping power is a function of the charge of the particle, the energy of the particle, and the material in which the charged particle interacts Stopping Power

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3/2003 Rev 1 I.3.1-2 – slide 9 of 20 Stopping power has units of MeV/cm – the amount of energy deposited per centimeter of material as a charged particle traverses the material It is the sum of energy deposited for both hard and soft collisions. S = = + S = = + Stopping Power dEdx Tot dE s dx dE h dx

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3/2003 Rev 1 I.3.1-2 – slide 10 of 20 Mass Stopping Power Often the stopping power is divided by the density of the material, This is called the “mass stopping power” The dimensions for mass stopping power are MeV – cm 2 g

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3/2003 Rev 1 I.3.1-2 – slide 11 of 20 Mass Stopping Power m 0 c 2 is the rest mass of the charged particle in MeV i.e. 3727 MeV for an alpha particle and i.e. 3727 MeV for an alpha particle and 0.511 MeV for an electron or beta particle 0.511 MeV for an electron or beta particle S = (0.3071) Zz 2 A2A2A2A2 13.8373 + ln - 2 – ln I 2222 (1- ) 2 moc2moc2moc2moc2 E 1 + 1 2 1 - ½ = = = =

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3/2003 Rev 1 I.3.1-2 – slide 12 of 20 Stopping Power Z = atomic number z = charge of the particle ( = 2, = 1) m 0 = rest mass of the particulate radiation c = speed of light (3 x 10 10 cm/s) I = the mean excitation potential of an atom of the absorbing material (2.16 x 10 -11 ) (Z)

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3/2003 Rev 1 I.3.1-2 – slide 13 of 20 Stopping Power Stopping power is used to determine dose from charged particles by the relationship: D = in units of MeV/g, where =the particle fluence, the number of particles striking an object over a specified time interval dE dx

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3/2003 Rev 1 I.3.1-2 – slide 14 of 20 Stopping Power Converting this to units of dose results in the relationship: D = (1.6 x 10 -10 ) Gy dE dx

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3/2003 Rev 1 I.3.1-2 – slide 15 of 20 Tissue Equivalent Stopping Power for Electrons Energy (MeV) 0.10.20.30.40.50.60.70.80.91.0 Mass Stopping Power, S/ (MeV-cm 2 )/g 4.22.82.42.22.02.01.91.91.81.8

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3/2003 Rev 1 I.3.1-2 – slide 16 of 20 Stopping Power Example Calculate the dose from a 37 kBq source of 32 P spread over an area of 1 cm 2 on the arm of an individual for 1 hour D = (1.6 x 10 -10 ) Gy Assume that 50% of the particles on the skin interact with the skin (2 geometry) dE dx

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3/2003 Rev 1 I.3.1-2 – slide 17 of 20 = (½)(37,000 Bq)(1 dis/s/Bq)(1 hr)(3600 s/hr) = 6.67 x 10 7 dis 32 P has a 0.6 MeV beta particle (average energy) For tissue equivalent plastic and a beta particle with an energy of 0.6 MeV, the stopping power is 1.96 MeV-cm 2 /g Stopping Power Example

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3/2003 Rev 1 I.3.1-2 – slide 18 of 20 D = (6.67 x 10 7 dis)(1.96 MeV-cm 2 )(1.6 x 10 -10 ) D = 0.021 Gy D = (1.6 x 10 -10 ) Gy dE dx 1 cm 2 g Stopping Power Example

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3/2003 Rev 1 I.3.1-2 – slide 19 of 20 Shielding

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3/2003 Rev 1 I.3.1-2 – slide 20 of 20 Where to Get More Information Cember, H., Johnson, T. E., Introduction to Health Physics, 4th Edition, McGraw-Hill, New York (2008) Martin, A., Harbison, S. A., Beach, K., Cole, P., An Introduction to Radiation Protection, 6 th Edition, Hodder Arnold, London (2012) Attix, F. H., Introduction to Radiological Physics and Radiation Dosimetry, Wiley and Sons, Chichester (1986) Firestone, R. B., Baglin, C. M., Frank-Chu, S. Y., Eds., Table of Isotopes (8 th Edition, 1999 update), Wiley, New York (1999)

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